Ok, let's start.
First, there are some games that you just can't win. These are the games where the accumulative pacing of all the enemies is higher than what you can manage, and this shows in situations where they are grouping on you, so any lead or outpacing you have done doesn't amount to much. But those games are not many. Maybe a 5% of the games you play, which is ok, I guess.
Next, like it or not, you have to comply with what the meta says. Assuming you are a player that is close to his real division or his peak and can't know for sure if you do deserve higher or not, you need to try and use any little thing you can to your advantage and avoid using things that might deter you away from winning. This means that if you use a champion whose winrate is low, it's just another obstacle. You might be very proficient at the champion, but there's only so much you can do with it, if your skill level is not head and shoulders above the rest of the competition, aka smurfing. I will give you a personal example.
I played quite a lot of Sivir on this account, and Sivir was on the weak side of ADCs. I still managed to have a decent win rate (60% or something over 50 games), because I do believe I'm better than the competition when I use this specific champion, since I think that I play Sivir to a level that is much higher than my current Plat 5. I can't do the same with other champions though, so I won't play Viktor anymore, who was on 47% winrate. At the same time, on my silver smurf, I can play whatever I want, as long as it meets the conditions above; a lot of damage, agency over the early game and mobility to create plays or avoid deaths. That's why I played a lot of assassin Jarvan, who has a lot of potential to shut down enemies completely and snowballs hard, or Graves who has insane 1v1 power, so I can invade the enemy jungle, shut down the enemy jungler etc.
Back to your GPM point, it's important to outpace the enemy in terms of gold, but you also need to look intohow you do XP-wise and also try to figure out when do you get all that gold. For example, when I play Sivir, I tend to try and cs as well as I can early game, but since her early laning phase is weak, sometimes I might have to drop cs, meaning my enemy will outpace me for some time during early-mid game, only for me to get a lot of gold later on when I get 2 items and start clearing things instantly and have enough time to rotate between lanes and get more gold etc. Do you see the problem, though? Even though I end up with something like 10cs/min and more gold than anyone else, I have to sacrifice a lot in the early game, meaning that the enemies can take advantage of that and destroy us during that stage, to the point that my good mid-late game might not matter at all. This can tie in with your Kassadin stats. You might be doing well later when you get your mana pool and level 16 and start one shotting people and try to be more aggressive and stuff, but until then, you are just handing over so many advantages to the enemy, that in the end, it might not matter.
Therefore, you need to try and keep a steady advantage over your enemies, so that you can impact the game and shut them down. That's why I find success as Janna support or Graves jungle. Those champions have the tools to outpace (yeah, the Janna support) the enemy laners /jungler, because with a strong early game opening (first minion wave or first jungle clear), you get to a point where your poke in lane or 1v1 in the jungle is strong enough to either get you kills or generally just set back and in some cases completely shut down the enemy. That's the power of an early game champion, who can then transition a lead into great powerspikes in the mid game and take over the game.
Also, another thing about GPM is that you might have a gold lead and outpace the enemy even at early levels, but do you outpace them hard enough? That's the thing and here comes the "some games are unwinnable" point. Sometimes, you have a big lead, but can do nothing about it, but there are other games where you might just not be using your gold lead and outpace enough, mostly because your champion doesn't allow it. This ties in with how I said you need to play champions with certain trais; mobility, damage, CC safety (range). For example, you can be fed as Volibear, but the fact that you are melee and have no reposition abilities means that in situations where you might have to dive, it might not be as easy. This means that even if you have a lead, the enemy can play safe and hug the tower and you can't really get much out of that lead. Instead, something a Graves can attack the enemy from range and burst them down quickly, while repositioning out of tower range with his E and R. He can also apply soft CC with his W from range as well.
As far as top lane and TP goes, I'm not quite sure. I tried to play some Shen this season (the ultimate support top laner), but it
didn't go well, even though I did really well last season with him. Maybe it was just unlucky games, but I didn't have much time to dedicate to try and play more games on him and see how it goes. Generally though, from what I read, top laners are not as important in this meta (not gonna talk about 8.11), therefore playing for lane with Ignite is risky. Sure, you might be able to get a lead in the top lane with it, you might even render the enemy top lane useless, but if you can't impact the part of the map that matters, then it's all for none. I don't like it more than you do, but maybe sometimes, you have to use your TP to affect the map. This ties in to what I said before; play champions that can impact the map. If the champion can't do that, then maybe taking teleport on them will.
The most important thing you have to understand is that whatever you do in the game, you need to:
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have agency over the game. Be able to create plays, be able to at least hold your own or even win 1v1s. Have the ability to fast clear waves / jungle so that you can win precious seconds over the enemy. That's extremely important. League is a game of seconds a lot of time. For example, as a jungler, if you can clear camps 1 second faster than your enemy jungler, it might make the difference between you taking the Scuttle Crab over the enemy. Same can be said about laners, where they might be able to sneak in some wards in the enemy jungle, or get faster on the roaming. That's why I consider Graves the best jungler. He has insanely fast and healthy clears, which means he can farm pretty fast, he can 1v1 because of that healthy clear and has a lot of damage, some mobility, can get tanky and has the W and red buff to apply good CC to gank or chase people. He has AGENCY over the game, he can MAKE THINGS HAPPEN. Amumu, instead, doesn't have the best clear, he is very mana reliable, his mobility and CC are tied to one spell (Q) which is a skillshot, so it's very unreliable, and he can't 1v1 anyone. See why Amumu is a very risky pick instead of Graves? Sure, he gets very tanky later and has a very strong ultimate, but that's only happening after a certain point of the game where you need to be able to force teamfights to get the maximum out of him, and by that time, Graves will have already decided he game.
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always be active and be in a position to do something productive. There's nothing worse than just pushing your lane, and then just waiting for the enemy laner to clear his under the tower and you wait there doing nothing. You need to pick something that can take advantage of that "free time" you have, be that someone who can poke, like Gnar, or someone that can go in the enemy jungle, ward or steal some camps and then get back in the lane to pick up the next wave. Again, this game is a game of seconds. Every second is precious when it's a race that you need to win, and having the tools to make the maximum of what time is given to you is important. This is also enhanced if the champion you play can utilize that time even better. For example, Maokai can clear a wave, but he can't really go and kill an enemy camp, so the only way he can make use of his "free time" is by warding, or a best take the Scuttle. Sure, it's something productive, but imagine a Jax who can go into the enemy jungle, take the enemy Red, for example, and go back to lane and get a big advantage, and in some cases, might even be able to 1v1 and kill the enemy jungler.
If you see which champions have the highest pick rate or win rate or are played in the professional scene, you will see some parallels between them. Ezreal is the most picked ADC with high win rates. Why?
- He's safe. He has a lot of poke, safety with his E, range on his AAs, global ulti to affect the map, be that through killing someone, or even picking up cs, and he has strong spikes during the first 5-20 minutes, so he can make things happen with his poke, damage and safety. The fact that he isn't a crit ADC, which means he doesn't deal as much damage late game as someone like Jinx doesn't really matter, because he has already decided the game by then.
Ornn is another pick. Why? He has an obnoxious laning phase; good wave clear with damage and a shield, good short trades, some mobility. He has the passive that acts as a safety net late game, because your allies can get 1000 gold stronger than the enemy because of the upgraded items and also his R, which is insane. Do you remember why Rumble was picked so often in seasons past? It's because he could be far away from a fight, but his huge range R was good enough damage and CC to assist the team and win fights. Ornn is kinda the same. He might be lacking the damage or range of Graves, but his devastating R is enough to make him extremely potent.
Taliyah. She has insane wave clear, strong mobility with her passive, great zoning with her rock field and CC with her knock back, while she can also have a semi-global with her R, that can also act as terrain to zone enemies away from things like towers, baron, dragon etc.
KhaZix. Invisibility (utility) means that he could not be spotted, so he could offer a lot of safe vision while ganking out of nowhere, with insanely strong damage.